Pentation

In mathematics, pentation (or hyper-5) is the next hyperoperation (infinite sequence of arithmetic operations) after tetration and before hexation. It is defined as iterated (repeated) tetration (assuming right-associativity), just as tetration is iterated right-associative exponentiation. It is a binary operation defined with two numbers a and b, where a is tetrated to itself b − 1 times. The type of hyperoperation is indicated by a number in brackets, []. For instance, using hyperoperation notation for pentation and tetration, ${\displaystyle 2[5]3}$ means tetrating 2 to itself 2 times, or ${\displaystyle 2[4](2[4]2)}$. This can then be reduced to ${\displaystyle 2[4](2^{2})=2[4]4=2^{2^{2^{2}}}=2^{2^{4}}=2^{16}=65,536.}$